Basic principles and applications of

ARPES and Spin-ARPES

Ivana Vobornik
CNR-IOM, APE Beamline @ Elettra,
AREA Science Park, Trieste, Italy
and NFFA Trieste
 Outline

• A brief introduction to photoemission

• History
• Theory
• Experimental requirements

• Valence band photoemission

• Refreshing solid state physics concepts
• ARPES
• Spin ARPES  complete photoemission experiment

• Complete photoemission experiment @ Elettra

• ARPES and Spin-ARPES station: @

 1887 - Photoelectric Effect

Observed by Heinrich Hertz 1887

- P. Lenard: measuring kinetic energy of photoelectrons in retarding field

Experimental observations:

- Measured photoelectron current increases with photon intensity

- Maximum energy of the (photo)electrons depends on light frequency (contrary

to classical expectation)
1905 – Explained by Albert Einstein
1905 – Photoelectric effect according to Einstein

- Electrons inside material absorb

incoming light quanta - photons

- If their energy is sufficiently high they

leave the material carrying info on their
properties inside the material

Photoemission
 Birth of photoemission 1950s

ideal tool for the chemical investigation of surfaces and thin film, expressed in the famous
acronym created by Siegbahn: ESCA (electron spectroscopy for chemical analysis)
or
XPS – X-ray Photoelectron/Photoemission Spectroscopy
Atom  Solid Cartoon

Localized core electrons

Localized core electrons

Delocalized valence
electrons (energy bands)
 What do we learn from photoemitted electrons?

Ekin  h  EB  

Core electrons (XPS):

composition, chemical bonding, valence, density of states, electronic correlations

Bi2Se3 topological insulator

C. Bigi, Master Thesis G. Panaccione et al.

Uni. Milano 2016 New J Phys 2011
 Experimental requirements for XPS (ESCA)

Laboratory Hemispherical electron

- X-rays - generated by energy analyzer
bombarding a metallic
anode with high-energy
electrons
- UV - noble gas
discharge lamps Channeltron
MCP
Synchrotrons detector
-Tunable and polarized
UVhard X-rays

Whatever you wish as Surface sensitivity -

long as sufficiently surfaces are an issue…
conductive…
 Experimental requirements – real life

End station of APE – LE beamline at Elettra

Sample
manipulator

Hemispherical
electron energy
analyzer
Sample surface
preparation
chamber

Photons

ARPES chamber
Surface sensitivity – electron mean free path

Bulk Bulk
Surface

UV Soft X
- Number of electrons reaching the surface is reduced by electron-electron scattering
Only sensitive to first couple of atomic layers!! Clean surfaces and UHV needed
- Scattered electrons with lower kinetic energies form background (secondaries)
Valence electron photoemission

ARPES

Spin-ARPES

Transport properties of a solids are determined by

electrons near EF (conductivity, magnetoresistance,
superconductivity, magnetism)
Valence band photoemission
Atom  Solid Cartoon

Localized core electrons

Localized core electrons

Delocalized valence
electrons (energy bands)
Real vs. reciprocal (momentum or k-)space

Free electron vs. electron in a lattice:

Periodic potential  electronic bands

and band gaps
p 2 ( k )2
E 
2m 2m
 Classification of materials according to the filling of the
electronic bands
E

EF

Metal
Semimetal
Semiconductor
Insulator

All this from E vs. k relation! And not only…

E

…when things get more

U
complicated and electrons EF
interact: fingerprints of
electronic correlations
Metal  Insulator
transition
Superconductivity
The question is…

Can E vs. k (i.e., the electronic band

structure of solids) be directly measured?

… and the answer…

Yes!
Valence band photoemission with angular resolution:
Angle-Resolved PhotoEmission Spectroscopy - ARPES
What do we learn from photoemitted valence electrons?

Energy conservation Momentum conservation

Ekin  h  EB   Inside the crystal:
k f  ki  kh
qout k f  ki
Refraction on the surface
(Snell’s law):

2m
kout  2
E kin

2m
kin  2
( E kin V0 )

2m 2m
kin||  kout ||  k||  sin out 2
E kin  sin in 2
( E kin V0 )
 What do we learn from photoemitted valence electrons?
qout
Measure:
- Kinetic energy of the photoemitted electrons
- Angle at which they are emitted
Ekin  h  EB  

Textbook example – the electronic band structure of copper:

} sp band

} d band

Courtesy of H. Dil
How do we handle the angle of the photoemitted electrons?

- Large angular acceptance (~30°)

- Analyzer electronic lenses keep

track of the electrons emitted at
different angles

- 2d detection (MCP)

 Dispersion along the analyzer slit

directly measured (i.e. dispersion
along one line in k space)
 Band mapping: 2d surface state on Au(111) surface
- 2d electron gas – parabolic disperion, circular Fermi contour - expected

- and measured by ARPES

EB = const
kx = const
ky = const
Back to textbooks: 1D  2D  3D
Fermi surface mapping – Fermi surface of copper

- 3d Fermi surface of Cu:

Almost (but not really) free electrons: the
sphere is not perfect – the necks connect
the spheres in the subsequent Brillouin
zones
Neck
- With single photon Distorted
energy ARPES sphere
measures a spherical
cut through the 3d
Fermi surface

Surface state Fermi

contour (perfect circle)
Principal boost to ARPES development

XXXXXXXX

20??

Searching for the E

mechanism of high Tc
superconductivity 
room temperature EF
superconductivity!!!

Metal Superconductor
 ARPES – stone age

High Tc cuprates:
Band mapping and Fermi
Superconducting gap:
surface mapping… by hand
X 

EF E
 Y  

Binding energy (eV)

a) b) c) 0.0

0.1
Photoelectron intensity

0.2

0.3
  

 Y
<20meV

0.4 0 0.4 0 0.4 0  

Binding energy (eV)
I. Vobornik et al.,
Phys. Rev. Lett. 82, 3128 (1999)

Energy resolution < 10 meV; angular resolution ~1°

I. Vobornik, PhD thesis, EPFL, Lausanne, 1999
   

ARPES evolution  Y

 

Milestone: Development of two 1994 P. Aebi et al.,

Phys. Rev. Lett. 72, 2757
dimensional detectors (1994)

P.V. Bogdanov et al., Phys. Rev. B 64

180505 (R) (2001), A. Bansil, M.
Lindroos Phys. Rev. Lett. 83 5154
(1999)

Images rather than spectra,

BUT still composed of spectra!!!

2004 A.A. Kordyuk et al.,

Phys. Rev. B 70, 214525
(2004)

20XX ?
Energy resolution ~1 meV; angular resolution ~0.1°
What do we learn from the ARPES SPECTRA?

Intuitive (NOT exact) three-step model of the photoemission process:

Three-step model: step 1

Transition probability from initial to final state

under the excitation by the photon with vector
potential A
2 e
f H int i  ( E f  Ei  h ) H int 
2
w fi  A p
mc

Optical transition in the solid:

- Energy is conserved
E f  Ei  h

- Wave vector is conserved modulo G

k f  ki  G
Three-step model: step 2
Inelastic scattering of the photoelectron with
• other electrons
(excitation of e‐h‐pairs, plasmons)
• phonons

- Generation of secondary electrons

"inelastic background"
- Loss of energy and momentum information
in the photoelectron current:
inelastic mean free path

Bulk Bulk
Surface

UV Soft X
Three-step model: step 3
The lowest energy electrons
can’t exceed the work function
potential

Ekin  h  EB  

Surface breaks crystal symmetry

k⊥ is not a good quantum
number

2m
kout  2
E kin

2m
kin  2
( E kin V0 )

2m 2m
kout ||  kin||  k||  sin out 2
E kin  sin in 2
( E kin V0 )
Exact one-step vs. intuitive three-step model

3 step model is strong

simplification; quantitative
description only possible by
matching wave function of
initial and final state
 Photoemission intensity is directly related with...
One particle Green’s function
describes the propagation of an extra electron (t>t’) (hole, t<t’)
added to the many body system
G ( xt , x' t ' )  i N ,0 T [ ( xt )  ( x' t ' )] N ,0

How?
Starting from the Fermi golden rule
the transition probability from the initial state N,0 to a final
state N,s with a photoelectron of energy  and momentum 
is given by

2

2
p (  )  N , s H int N , 0  ( EsN  E0N   )  ...
s

Dipole approximation, Sudden approximation - the photoelectron is instanteneously

created and decoupled form the remaining N-1 electron system

2 2 1
...  M k A( ,  )  Im G  ( ,  )
2 2
M k

Beyond images– spectral line-shape & electronic correlations

2
I (k ,  )  f A  p i A(k ,  ) f ( )
1
f ( )   
1 e kT

 1 
G (k , )  ,  0 G (k , ) 
1

   k  i    k   (k , )

  1 Im (k , )
A(k , )   (   k ) A(k , ) 
     Re (k, ) 2  Im (k, ) 2
k
Matrix elements – orbital character of the bands

2
I (k ,  )  f A  p i A(k ,  ) f ( )

The light beam and the

analyser define the scattering
plane.
If to be detected, the
photoelectron final state has to
be even under reflection in the
scattering plane.
Access to the symmetries (i.e.
Orbital character) of the initial
state in the solid
Prevalent s- or p- character of the Be(0001) surface states

I. Vobornik et al., PRB 2005, PRL 2007

 ARPES w/ synchrotron radiation: powerful tool in
investigation of electronic properties of materials
– electronic band structure, orbital character, correlations

qout

Courtesy of
M. Grioni
GeTe, C. Rinaldi et al., Nano Letters 2018

WTe2, P. Das, D.
DiSante et al.,
Nat. Comm.
2016; PRL 2018

PdTe2, M.S. Bahramy, Nature Materials 2018

Dirac dispersion and Fermi surface in PbBi6Te10 Au(001) surface states ZrTe5 band structure
M. Papagno et al., ACS Nano 2016 S. Bengio et al. PRB 2012 G. Manzoni et al., PRL 2016
 ARPES and 21st century materials

1994

Electronic materials
Spintronic materials
2004 Functional materials

QUANTUM materials!
 2004: graphene came into scene
The thinnest possible material - only one atom thick
Ballistic conduction - charge carriers travel for m w/o scattering
The material with the largest surface area per unit weight – 1 gram of graphene can cover
several football stadiums
The strongest material – 40 N/m, theoretical limit
 The stiffest known material - stiffer than diamond
The most stretchable crystal – can be stretched as much as 20%
The most thermal conductive material - ~5000 Wm-1K-1 at room temperature
Impermeable to gases – even for helium
Dirac electrons enter the condensed matter physics…

Conical (linear) Dirac dispersion and point-like Fermi surface measured by ARPES:

S. Y. Zhou et al., Nature Physics 2, 595 (2006)

A. Bpstwick et al., Nature Physics volume 3, pages 36 (2007)

 … and not only in graphene: topological insulators

Quantum Hall state Conical (linear) Dirac dispersion

and
Spin-momentum locking

Quantum spin Hall state

Characterized with well

defined spin texture

3D case

The technique of choice:

Spin-ARPES !
C. Kane & J. Moore, Physics World, Feb.2011, 32
… more textbooks  beyond Ashcroft-Mermin/Kitell

The concepts of high energy

physics within
condensed matter!
Quantum Materials in 20th century
E

U
EF

Metal Metal  Insulator

Semimetal transition
Semiconductor (High Tc)
Insulator superconductivity

Quantum Materials in 21st century

 Transition metal dichalcogenides (TMDCs)

Three dimensional
schematic presentation of
typical MX2 structure

M = transition metal
X = S, Se or Te

• Layered structure with strong intra-layer covalent bonding and weak (van der
Waals type) inter-layer coupling

• Exhibit wide variety of physical properties – semimetals (WTe2, TiSe2), metals

(NbS2, VSe2), semiconductors (MoS2, MoSe2), superconductors (NbSe2, TaS2)

• Properties often conditioned by the number of layers

• Host spin polarized electrons and /or Dirac/Weyl fermions

Quantum Materials in 21st century – High energy
physics concepts within condensed matter

• Low-dimensional materials (2D, surfaces, few atomic layers)

• The Bloch wave functions follow Dirac-like or Weyl-like
equations at vicinity of some special points of the Brillouin
zone
• Envisioned applications: spintronics, quantum computing, etc.

• The materials characterized by particular spin texture 

ARPES Milestone : High-resolution Spin-ARPES
 What else do we learn from photoemitted electrons?
qout 2m
kout  2
E kin

2m
kin  2
( E kin V0 )

2m 2m
kin||  kout ||  k||  sin out E kin  sin in ( E kin V0 )
Ekin  h  EB   2 2

Spin:
magnetism, spin texture in the systems with strong spin-orbit interaction

Spin - ARPES: E(k), Spin

Complete set of quantum numbers of photoemitted electron

Complete photoemission experiment!

Exchange-split spin-polarized bands in ferromagnetic iron

E. Kisker et al. Phys. Rev. B 31, 329 (1985)

Detecting electron’s spin: spin-dependent scattering

MOTT scattering VLEED scattering

 spin-orbit interaction  magnetic exchange interaction

 left-right asymmetry  parallel-antiparallel asymmetry
 >25keV  <15eV
 commercial  non-commercial
 Au target  FeO target
 FOM 10-4  FOM 10-2
Target magnetization dependent intensity asymmetry
between spin up and spin down electrons

If the target is magnetized

Up / Down, the incoming
electrons with spin-up/down will
be reflected more (top/bottom
panel)

If the primary beam is polarized,

then non-zero asymmetry
value will be measure.

Resulting ARPES spectra 

 Spin-integrated vs. spin-resolved ARPES

Spin Spin
integrated resolved
Au(111) Au(111)
surface surface
state state

Spin integrated Spin resolved

Bi2Se3 Bi2Se3
topological topological
surface state surface state
VLEED based spin-ARPES scheme

Two scattering chambers

In each two orthogonal

directions of spin can be
measured

Vectorial (3d) spin analysis

Magnetization coils outside… … and inside the scattering chamber
 VESPA: spin polarimeter @ APE

 VESPA: Very Efficient Spin Polarization Analysis

 Designed, built and commissioned in Trieste

(CNR-IOM, NFFA)

 Operates from Dec. 2015 at APE beamline @ Elettra

 APE: Advanced Photoelectric effect Experiments

Two independent, off-axis, variable polarization (APPLE type) undulators

two independent canted beamlines operating simultaneously
First users: 2003

• APE – High Energy (150-1600 eV)

– XPS spectroscopy
– X-ray absorption (XAS, XMCD, XMLD)

• APE – Low Energy (8-120 eV)

– High-resolution ARPES @ Spin-ARPES
– Electronic band structure
– Fermi surface mapping
– Fermi surface instabilities
 APE surface science laboratory
Omicron EA125
APE-HE

Variable polarization
photons 150-1600 eV Distribution
center

Users’ docking ports

STM

S segregation on Fe(100)
Load-lock MO Kerr effect;
LEED/Auger
Sample preparation Sample growth and prep.

APE-LE
Variable polarization
photons 8-120 eV

VG Scienta DA30 analyzer

+ 2 VLEED spin polarimeters
Fe(100) Fermi surface
 Complete Photoemission Experiment @ beamline APE
 APE – High Energy (150-1600 eV)
– XPS spectroscopy
– X-ray absorption (XAS, XMCD, XMLD)
– NEW: Spectroscopy in-operando
and ambient pressure

 APE – Low Energy (8-120 eV)

– High-resolution ARPES
– Electronic band structure
– Fermi surface mapping
– Fermi surface instabilities
– NEW: Spin-resolved ARPES
 Spin-resolved ARPES at beamline APE (CNR-IOM, NFFA)
In search for spin polarized electrons for future spintronic materials

 VESPA: Very Efficient  Some recent results:

Spin Polarization Analysis Maximazing Rashba-like spin
 Designed, built and splitting in PtCo2
commissioned in Trieste V. Sunko et al., Nature 549, 492–496
(CNR-IOM, NFFA) (2017)
 Operates from 2015 at APE Surface induced symmetry breaking enhances
beamline @ Elettra spin-orbit interaction and induces spin
 C. Bigi et al. JSR (2017) 24, polarized electrons on the surface of PtCo2.
750-756, on the title page
of JSR: Co‐existence of type‐I and
type‐II three dimensional
bulk Dirac fermions in PdTe2
M.S. Bahramy et al.,
Nature Materials, 2018
Spin-resolved ARPES data confirm
the helical spin texture of the two
surface states in PdTe2 and therefore
their topological nature.

Weyl electrons on the surface of MoTe2

J. Jiang et al., Nature Communications 8,
13973 (2017)
Measured spin polarization provides evidence of
the presence of Weyl electrons in MoTe2.
Latest result: Spin- Fermi surface mapping

O.J. Clark et al., PRL 2018

After this lecture…

 feeling of what ARPES and Spin-ARPES can do for you

 If interested in quantum properties of materials - electronic band

structures, Fermi surfaces, electronic correlations, spin
polarization:

http://www.elettra.trieste.it/elettra-beamlines/ape.html

http://www.trieste.nffa.eu/
 Interested in learning more?

• ARPES:
• S. Hüfner, Photoelectron Spectroscopy – Principles and Applications, 3rd ed.
(Berlin, Springer, 2003)
• S. Suga, A. Sekiyama, Photoelectron Spectroscopy – Bulk and Surface
Electronic Structures (Berlin, Springer, 2014)

• F. Reinert and S. Hüfner, New Journal of Physics 7, 97 (2005)

• A. Damascelli, Physica Scripta T109, 61 (2004)
• S. Hüfner et al., J. Electron Spectrosc. Rel. Phen. 100, 191 (1999)

• Spin-ARPES:
• Taichi Okuda, J. Phys.: Condens. Matter 29 483001 (2017)
• Chiara Bigi et al., J. Synchrotron Rad. 24, 750-756 (2017)
 Photoemission relations

Ekin  h  EB  

2 2
w fi  f H int i  ( E f  Ei  h )

e
H int  A p
mc

2
I (k ,  )  f A  p i A(k ,  ) f ( ) 2m
kout  2
E kin
1 Im (k ,  )
A(k ,  )  2m
     Re (k ,  ) 2  Im ( k ,  ) 2 kin  ( E kin V0 )
k 2

1
f ( )  2m 2m
 
kout ||  kin||  k||  sin out E kin  sin in ( E kin V0 )
1 e kT 2 2